Question

Select the relation that IS a function.

a) {(-6, -5), (3, 2), (10, 8), (3, 3)}
b) {(-2, -1), (5, -1,) (16, 3) (-3, -9)}
c) {(5, 10), (-3, 10), (-3, -10), (4, 7)}
d) {(21, 11), (21, 10), (21, 9), (21, 8)}

Answer 1

A relation is a function if each x-value has a unique y-value. Option b) {(−2, −1), (5, −1,), (16, 3), (−3, −9)} is the only relation among the given options that is a function.

Step-by-step explanation:

A relation is a function if, for every input value, there is only one output value. In other words, each x-value in the relation must have a unique corresponding y-value. Looking at the given options:

a) {(-6, -5), (3, 2), (10, 8), (3, 3)} - This option is not a function because there are two different y-values (2 and 3) for the same x-value (3).

b) {(-2, -1), (5, -1,) (16, 3) (-3, -9)} - This option is a function because each x-value has a unique y-value.

c) {(5, 10), (-3, 10), (-3, -10), (4, 7)} - This option is not a function because there are two different y-values (10 and -10) for the same x-value (-3).

d) {(21, 11), (21, 10), (21, 9), (21, 8)} - This option is not a function because there are four different y-values (11, 10, 9, and 8) for the same x-value (21).

Therefore, the relation that IS a function is option b) {(−2, −1), (5, −1,), (16, 3), (−3, −9)}.